The present invention relates to a beam splitting optical element which divides an incident beam into a plurality of number of emitted beams, and more particularly, to a beam splitting optical element using diffractive gratings.
Conventionally, beam splitters using diffractive gratings have been known. In such beam splitters, linear grooves or raised portions (i.e., gratings) are formed on, for example, a glass substrate. The arrangement of the gratings determines the pattern of emitted diffracted beams. Typically, the emitted beams (xc2x11st order beams, xc2x12nd order beams, . . . ) are arranged symmetrically around a central beam (i.e., a zero order diffracted beam) and, as a result, there are an odd number of diffracted beams emitted.
A diffraction efficiency of the conventional diffractive gratings as described above is generally in a range of 70%-85%. There is a need for a beam splitter employing diffractive gratings which has a relatively high diffraction efficiency.
Further, in the field of digital opto-electronics, it is particularly useful if a diffractive optical element has an even number of emitted beams having relatively similar intensities. For example, in an optical recording device accessed by a computer or an optical computer, eight bits (a byte) is a unit when data is processed. If a beam is divided into an even and desired number of beams by the beam splitter, it is advantageous since the emitted beams are used for processing the data efficiently.
It is therefore an object of the present invention to provide an improved beam splitting optical element which divides an incident beam into an even number of beams and has a higher diffraction efficiency than a conventional element.
For the above object, according to one aspect of the invention, there is provided a diffractive optical element, comprising a cylindrical surface provided with a diffractive grating pattern. The diffractive grating pattern includes a plurality of phase gratings arranged in parallel lines extending along a circumference of the cylindrical surface to cause diffraction of an incident beam, where a beam incident on the diffractive grating pattern is emitted as divided into a plurality of diffracted beams. Since the grating pattern is formed on a cylindrical surface, and the garatings extend along the circumference of the cylindrical surface, a mold to be used for molding the grating pattern can be made easily with use, for example, a lathe.
Preferably, a surface of the optical element from which the diffracted beams are emitted is also cylindrical having a curvature that is substantially the same as a curvature of the cylindrical surface, so that the phase diffracting element has a meniscus shape and has substantially no magnifying power in total.
Optionally, the plurality of phase gratings are of equal width in a direction of the generatrix of the cylinder and each of the plurality of phase gratings has a continuous, nonlinear surface to cause phase differences in a wave front of the incident beam. The mold for such a grating can be made relatively easily when the lathe is used.
Further optionally, each of the plurality of phase gratings has an asymmetrical phase pattern, and a phase gap xcex94P, representing a phase difference between an end point of each of the plurality of phase patterns and a beginning point of each of the plurality of phase patterns, in radians. The phase gap, xcex94P, is substantially equal for each of the plurality of phase gratings and satisfies:
0.7xcfx80 less than |xcex94P| less than 1.2xcfx80. 
With this structure, the emitted beams (i.e., the diffracted beams) distribute asymmetrically with respect to the zero order diffracted beam, and accordingly, it is possible that the number of diffracted beams can be adjusted to an even number.
Further optionally, the plurality of phase gratings are adjusted so that each of the divided diffracted beams have substantially the same intensity and no divided beam is omitted other than the intended number of beams. As a result, an even number of diffracted beams have substantially the same intensity may be emitted from the diffractive optical element.
According to another aspect of the invention, there is provided a diffractive optical element, comprising a base plate provided with a diffractive grating pattern. The diffractive grating pattern includes a plurality of phase gratings arranged in parallel lines extending along a predetermined direction of the base plate to cause diffraction of an incident beam. A beam incident on the diffractive grating pattern is emitted as a plurality of diffracted beams, wherein each of the plurality of phase gratings has an asymmetrical phase pattern in a direction where the plurality of phase gratings are arranged A phase gap xcex94P, representing a phase difference between an end point of each of the plurality of phase patterns and a beginning point of each of the plurality of phase patterns, in radians, is substantially equal for each of the plurality of phase gratings and satisfies:
0.7xcfx80 less than |xcex94P| less than 1.2xcfx80. 
With this optical element, a desired even number of diffracted beams, which are asymmetrically distributed with respect to the zero order beam, are obtained.
It should be noted that the diffracted beams substantially consist of a desired number of beams.
Various examples are indicated as embodiments. In each embodiment, a predetermined error in the phase pattern is permissible.
Specifically, the predetermined permissible error in the phase difference may be less than 2%.
According to a further aspect of the invention, there is provided a diffractive optical element, comprising: a base plate having a cylindrical surface; and a diffractive grating pattern engraved on the cylindrical surface in a direction perpendicular to a generatrix of the cylindrical surface so that diffracted beams distribute in a dimension along the generatrix.
Since the diffractive grating pattern is formed on the cylindrical surface, a mold to be used for molding the optical element can be produced relatively easily.
Optionally, the grating pattern includes a plurality of phase gratings. Due to the shape of the optical element, and therefore the shape of the mold for the optical element, a complicated pattern can be employed. Accordingly, the grating can be a phase grating. When employing the phase grating, diffraction efficiency is improved.
Optionally or alternatively, each of the phase gratings has an asymmetrical phase pattern. As a result, the diffracted beams distribute asymmetrically with respect to a zero order diffracted beam.
Accordingly, by selecting an appropriate phase pattern of the phase gratings, an even number of diffracted beams can be emitted.
According to a further aspect of the invention, there is provided a method for producing a diffracting optical element, comprising: making a mold by (1) rotating a cylindrical metal mold about a rotation axis, and (2) moving a cutting tool to a predetermined radial distance from the rotation axis and moving the tool along the rotation axis; and applying an injection mold process with use of a master made by the steps in making the mold to make the diffracting optical element.
With this method, a complicated phase pattern can be formed on the mold.
According to a further aspect of the invention, there is provided a method for producing a mold to be used for making a diffracting optical element having a cylindrical surface with an injection mold process, comprising (1) rotating a cylindrical metal mold about a rotation axis, and (2) moving a cutting tool to a predetermined radial distance from the rotation axis and moving the tool along the rotation axis. Also with this method, a complicated pattern extending along a circumference of the mold can be formed on the circumferential surface of the mold.